Area of Effect

Area of Effect, or AoE, are spells which affect more than one target within a pre-determined radius set by the game's mechanics. These effects range from HoT spells to DD spells and cover all points in between. Traditionally (as far as MMORPGs go), the anchor target (location at which the caster is aiming the spell), and those closest to that target, are affected the most by the AoE effect, with diminishing returns as the spell radiates outward. In World of Warcraft, most area spells are GTAoE or PBAoE, and all targets in the area suffer the full effect.

Some AoE effects are cast or used without having to target someone or something; the caster is the anchor for the spell. The effect/damage radiates outward from the caster up to a given range, affecting all targets, or the first given number of targets the expanding 'ring' impacts. These types of spells are referred to as PBAoE, which stands for Point Blank Area of Effect.

Caster classes that are weak physically tend to have powerful PBAoE spells (if granted by their class). These sorts of spells require them to be right next to multiple hostile targets, so the spells are designed to be worth the danger.
Melee- and tank-type classes are usually designed to take damage from multiple targets, and as such their PBAoE-type abilities tend to be very weak.

The perhaps most versatile version in WoW is the mage spell Arcane Explosion. A mage can run into the middle of a group of otherwise distracted mobs (perhaps by a tank holding their aggro) and start blasting away (or just start blasting without a tank, while a healer frantically keeps him alive). A few PBAoEs from a higher-level casters can normally take an entire crowd of enemies out.

With Ground Targeted Area of Effect (GTAoE) spells, the player places a circle on the ground that will be the area of the spell effect. He carefully places this around his targets and clicks to start casting/channeling. All enemies that are in that area – or remain in that area for channeled or damage-over-time GTAoEs – suffer the damage. Some examples: Blizzard, Flamestrike, Freeze, Hurricane, Rain of Fire, Volley. One exception is the Death Knight spell, Death and Decay, which you target the circle for, click, then let the spell run its course without the need to channel. Another exception is the Shaman spell Fire Nova, in which no area is selected, rather the enemies around the fire totem will be damaged instantly.

The targeting circle that appears on the ground when casting many AoE spells.

All area effect damage effects will have 'area damage caps' in patch 2.2.0 which limit the number of targets which will be affected by any AoE effects. There are already spells, such as Arcane Explosion (AE), using these to a certain extent. In the case of AE, the damage decreases per mob, up until about 15 mobs being, at which point it holds at a certain amount of minimum damage.